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vectors lie along the same straight line |
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lines of action meeting at common point |
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lines of action do not pass through a common point |
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lines of action all lie within the same plane |
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Load (p): a force applied to a body (also called an external force) Stress (f): the resistance of a body to a load (also called an internal force) and measured in kips (K) |
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stress/unit of area at the section, measured in psi or ksi (kips/sq.in.) |
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the deformation of a material caused by external loads. Tensile loads stretch, and compressive loads shorten. |
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a strain produced by pressure in the structure when its layers are lateral shifted in relation to each other |
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the tendency of a force to cause rotation about a given point or axis |
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a material’s resistance to non permanent (or elastic) deformation |
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the force acting at the supports of a beam that holds it in equilibrium |
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A load imposed on a structural member at some point other than the centroid of the section |
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measure of an object’s resistance to changes to its rotation. |
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the ratio of a cross section's second moment of area to the distance of the extreme compressive fibre from the neutral axis |
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unit stress is proportional to unit strain up to the elastic limit |
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the amount of stress that causes a material to deform without additional load added |
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Composite Structural Member |
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more than one material working together (eg: reinforced concrete, box beam, flitch beam) |
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ability of material to absorb energy while undergoing elastic range stresses |
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Stress (f) = Total Force (P) / Area (A) |
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Force Equations - To find force |
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Force (F) = Mass (M) x Acceleration (a) F = Ma |
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Force Equations - To find shear diagram shear force |
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Shear Resisting Force (R) = (V) = uniform load per foot (w) x distance (L) / 2 R=V=wL/2 |
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Force Equations - To find the horizontal force on a retaining wall |
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Force(F) =soil pressure(w) x height of wall(h)2 /2 F=w(squared)h/2 |
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Moment Equations - To find equilibrium by taking moments about a point |
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Moment Equations - To find the eccentric load |
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M = Pe (the same as finding equilibrium) |
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Moment Equations - To find uniform load |
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Moment Equations - To find point/concentrated load at the center of a member |
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Moment Equations - To combine Point Load and Uniform Loads |
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Section Modulus Equations - To find Section Modulus |
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(both moment and stress are in kips or lbs) SectionModulus(S)=Base(b) x diameter(d)^2 /6 S=bd^2 /6 Section Modulus (S) = Moment (M) / Bending Stress (Fb) S = M / Fb Section Modulus (S) = Moment of Inertia / given constant (c) S = I / c |
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Section Modulus Equations - To find Section Modulus for a roof beam |
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Section Modulus (S) = Moment (M) / 1.25 x Bending Stress (Fb) S = M / 1.25Fb |
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Moment of Inertia Equations - To find Moment of Inertia |
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(occurs about the centroidal axis) Moment of Inertia(I)= Base(b) x depth(d)^3 /12 I=bd^3 /12 |
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Moment of Inertia Equations - To find Rectangle Moment of Inertia |
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Rectangle Moment of Inertia (I) = Base (b) x depth (d)^3/ 3 I = bd^3 / 3 |
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Moment of Inertia Equations - To find Moment of Inertia at base |
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(Ibase) = Moment of Inertia (I) + Area (A) x distance from centroid to base (y)^2 Ibase = I + Ay^2 |
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